Understanding the behaviour of physical systems undergoing a continuous phase transition at and near their critical point is one of the major challenges of modern statistical physics, both on the physics and the mathematical sides. In the first half of the twentieth century, the understanding relied essentially on exact computations, as exemplified by the analysis of mean-field systems and Onsager's revolutionary solution of the 2D Ising model [1]}. In the sixties, the arrival of the renormalization group (RG) formalism (see [2]} for a historical
exposition) led to a (non-rigorous) deep physical and geometrical understanding of continuous phase transitions. The RG formalism suggests that “coarse-graining” renormalization transformations correspond to appropriately changing the scale and the parameters of the model under study. The large scale limit of the critical regime then arises as the fixed
point of the renormalization transformations.
